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INVESTIGATIONS ON SOME PLANAR
MICROWAVE FILTERS
A Thesis submitted in partial fulfillment of the Requirements for the degree of
Master of Technology
In
Electronics and Communication Engineering
Specialization: Communication and Networks
By
KATTA SARAN KRISHNA
Roll No. : 212EC5167
Department of Electronics and Communication Engineering
National Institute of Technology Rourkela
Rourkela, Odisha, 769 008, India
27th May 2014
INVESTIGATIONS ON SOME PLANAR
MICROWAVE FILTERS
A Thesis submitted in partial fulfillment of the Requirements for the degree of
Master of Technology In
Electronics and Communication Engineering
Specialization: Communication and Networks
By
Katta Saran Krishna
Roll No. : 212EC5167
Under the Guidance of
Prof. Santanu K. Behera
Department of Electronics and Communication Engineering
National Institute of Technology Rourkela
Rourkela, Odisha, 769 008, India
27th May 2014
Dedicated to My family
DEPT. OF ELECTRONICS AND COMMUNICATION
ENGINEERING
NATIONAL INSTITUTE OF TECHNOLOGY, ROURKELA
ROURKELA – 769008, ODISHA, INDIA
Certificate
This is to certify that the work in the thesis entitled Investigations on Some Planar
Microwave filters by Katta Saran Krishna is a record of an original research work carried
out by him during 2013 - 2014 under my supervision and guidance in partial fulfillment of
the requirements for the award of the degree of Master of Technology in Electronics and
Communication Engineering (Communication and Networks), National Institute of
Technology, Rourkela. Neither this thesis nor any part of it, to the best of my knowledge,
has been submitted for any degree or diploma elsewhere.
Place: NIT Rourkela Dr. Santanu K. Behera
Date: 27th May 2014 Associate Professor
DEPT. OF ELECTRONICS AND COMMUNICATION
ENGINEERING
NATIONAL INSTITUTE OF TECHNOLOGY, ROURKELA
ROURKELA – 769008, ODISHA, INDIA
Declaration I certify that
a) The work contained in the thesis is original and has been done by myself under the
general supervision of my supervisor.
b) The work has not been submitted to any other Institute for any degree or diploma.
c) I have followed the guidelines provided by the Institute in writing the thesis.
d) Whenever I have used materials (data, theoretical analysis, and text) from other
sources, I have given due credit to them by citing them in the text of the thesis and
giving their details in the references.
e) Whenever I have quoted written materials from other sources, I have put them under
quotation marks and given due credit to the sources by citing them and giving
required details in the references.
Katta Saran Krishna
27th May 2014
i
Acknowledgement
It is my immense pleasure to avail this opportunity to express my gratitude, regards and heartfelt
respect to Prof. Santanu K. Behera, Department of Electronics and Communication Engineering,
NIT Rourkela for his endless and valuable guidance prior to, during and beyond the tenure of the
project work. His priceless advices have always lighted up my path whenever I have struck a dead
end in my work. It has been a rewarding experience working under his supervision as he has always
delivered the correct proportion of appreciation and criticism to help me excel in my field of
research.
I would like to express my gratitude and respect to Prof. S. K. Behera, Prof. K. K. Mahapatra,
Prof. S. Meher, Prof. P. Singh, Prof. S. Ari, Prof. S. Maiti, Prof. A.K. Sahoo, Prof. S. Hiremath,
Prof. A. Swain, and Prof. S. K. Das for their support, feedback and guidance throughout my M.
Tech course duration. I would also like to thank all the faculty and staff of ECE department, NIT
Rourkela for their support and help during the two years of my student life in the department.
I would like to make a special mention of the selfless support and guidance I received from my
senior’s Y. K. Choukiker, Runa Kumari, department of Electronics and Communication
Engineering, NIT Rourkela during my project work.
Last but not the least; I would like to express my love, respect and gratitude to my parents, elder
brother, who have always supported me in every decision I have made, guided me in every turn of
my life, believed in me and my potential and without whom I would have never been able to
achieve whatsoever I could have till date.
KATTA SARAN KRISHNA
ii
Abstract
Filters are substantial microwave components. RF/Microwave filters can be implemented using
transmission lines. In this thesis microstrip bandpass filters had been designed for RF/microwave
applications. Some novel techniques like implementing the open split koch loop resonators, open
split square loop resonators, and star shaped multi-mode resonators are implemented in designing
the microstrip bandpass filters. Microstrip filters are used in this report to design bandpass filters
because of their compact sizes.
The goal of this thesis is to investigate on some planar microwave bandpass filters. In this thesis
four novel compact bandpass filters has been designed and simulated, specifically three pole koch
resonator, seven pole koch resonator, three pole square loop resonator and compact UWB bandpass
filter using MMR. The design and simulation of each and every filter is given in detail with
including all the required specifications. From the previous research studies it is evident that, to
design a good bandpass filter there should be a smooth passband and good stopband with higher
insertion loss in the stopband. The four designs which are explained in this thesis has these
important factors, which makes these filters useful for the microwave applications.
iii
Contents
Acknowledgement ........................................................................................................................................ i
Abstract ........................................................................................................................................................ ii
Contents ...................................................................................................................................................... iii
List of Figures .............................................................................................................................................. vi
List of Tables .............................................................................................................................................. vii
CHAPTER ONE ........................................................................................................................................... 1
Introduction ................................................................................................................................................. 1
1.1 Microwave Communication: ......................................................................................................... 1
1.2 Definition of a Filter ..................................................................................................................... 3
1.3 Role of filters in microwave communication ................................................................................ 4
1.4 Applications of filters ................................................................................................................... 4
1.5 Satellite filters ............................................................................................................................... 5
1.6 Microwave filters in cellular communication ............................................................................... 5
1.7 Literature review on Microwave filters......................................................................................... 6
1.8 Organization of Thesis .................................................................................................................. 8
CHAPTER TWO .......................................................................................................................................... 9
Basic concepts of Transmission Lines ....................................................................................................... 9
2.1 Microstrip Lines ............................................................................................................................ 9
2.1.1 Structure of the Microstrip .................................................................................................... 9
2.1.2 Waves in Microstrip .............................................................................................................. 9
2.1.3 Quasi-TEM Approximation ................................................................................................ 10
2.1.4 Guided Wavelength, Propagation Constant, Phase Velocity, and Electrical Length .......... 11
2.1.5 Dispersion in Microstrip ..................................................................................................... 12
2.1.6 Losses in Microstrip ............................................................................................................ 13
2.1.7 Enclosure Effect .................................................................................................................. 13
2.1.8 Higher order modes and Surface Waves ............................................................................. 14
2.2 Coupled microstrip lines ............................................................................................................. 14
2.2.1 Design Equations ................................................................................................................ 16
2.3 Discontinuities in Microstrip ...................................................................................................... 18
iv
2.4 Microstrip Components............................................................................................................... 19
2.5 Resonators ................................................................................................................................... 21
CHAPTER THREE .................................................................................................................................... 23
Types of Microstrip Filters and Their Applications .............................................................................. 23
3.1 Lowpass and Bandpass Filters .................................................................................................... 23
3.1.1 Lowpass Filters ................................................................................................................... 23
3.1.2 Bandpass Filters .................................................................................................................. 23
3.2 Highpass and Bandstop Filters .................................................................................................... 24
3.2.1 Highpass Filters................................................................................................................... 24
3.2.2 Bandstop Filters .................................................................................................................. 24
3.3 Coupled-Resonator Circuits ........................................................................................................ 25
3.4 Filter Miniaturization and Compact Filters ................................................................................. 25
3.5 Ultra-Wideband Filters ............................................................................................................... 26
3.6 Electronically Tunable and Reconfigurable Filters ..................................................................... 26
3.7 Advanced RF/Microwave Filters ................................................................................................ 27
3.8 High-Temperature Superconducting (HTS) filters ..................................................................... 28
CHAPTER FOUR ....................................................................................................................................... 29
Design of Bandpass filters Using Open split Resonators ....................................................................... 29
4.1 Introduction ................................................................................................................................. 29
4.2 Koch curve .................................................................................................................................. 31
4.3 Filter designs ............................................................................................................................... 32
4.3.1 A Three pole Open Split Koch Loop Resonator (OSKLR) ................................................ 32
4.3.2 Seven pole Open Split Koch Loop Resonator (OSKLR) .................................................... 36
4.3.3 Three Pole Element Compact Open Loop Square Resonator ............................................. 40
4.4 Conclusion .................................................................................................................................. 43
4.5 Comparison between the three filters .......................................................................................... 44
CHAPTER FIVE ........................................................................................................................................ 45
Compact UWB Star Shaped Multiple-Mode Resonator for Bandpass Filter with Enhanced Upper-
Stopband Performance ............................................................................................................................. 45
5.1 Introduction ................................................................................................................................. 45
5.2 Filter characterization ................................................................................................................. 46
5.3 Dimensions of the filter............................................................................................................... 47
5.4 Simulated Results ........................................................................................................................ 48
v
5.5 Conclusion .................................................................................................................................. 48
CHAPTER SIX ........................................................................................................................................... 49
Conclusion and Future work ................................................................................................................... 49
5.1 Conclusion .................................................................................................................................. 49
6.2 Future Work ................................................................................................................................ 50
REFERENCES .......................................................................................................................................... 51
vi
List of Figures
Figure 1. 1 Electromagnetic spectrum .......................................................................................................................... 2
Figure 2. 1 Broad microstrip structure ........................................................................................................................ 10
Figure 2. 2 Cross sectional view of the pair of coupled microstrip lines .................................................................... 14
Figure 2. 3 Quasi-TEM modes of a coupled microstrip lines pair .............................................................................. 15
Figure 2. 4 Discontinuities in microstrip .................................................................................................................... 19
Figure 2. 5 Lumped-element inductors ....................................................................................................................... 20
Figure 2. 6 Lumped-element capacitors ...................................................................................................................... 21
Figure 2. 7 Some typical microstrip resonators .......................................................................................................... 22
Figure 4. 1 Koch curve ................................................................................................................................................. 31
Figure 4. 2 Open Split Koch Loop Resonator ............................................................................................................. 32
Figure 4. 3 Design and dimensions of the simulated five pole OSKLR slow-wave filter .......................................... 33
Figure 4. 4 S-Parameter of the designed filter ............................................................................................................ 34
Figure 4. 5 OSKLR ..................................................................................................................................................... 36
Figure 4. 6 Design and dimensions of the filter .......................................................................................................... 37
Figure 4. 7 S-Parameter of the designed filter ............................................................................................................ 38
Figure 4. 8 Open Loop Square Resonator ................................................................................................................... 40
Figure 4. 9 Design and dimensions of the simulated three pole OLSR filter .............................................................. 41
Figure 4. 10 S-Parameter of the designed filter .......................................................................................................... 42
Figure 5. 1 Schematic of the UWB BPF ..................................................................................................................... 46
Figure 5. 2 Equivalent transmission line network for the proposed UWB BPF ......................................................... 46
Figure 5. 3 Simulated frequency responses of the proposed BPF ............................................................................... 47
vii
List of Tables
Table 1.1 Frequency bands ........................................................................................................................................... 3
Table 4. 1 Dimensions of the three pole OSKLR ........................................................................................................ 34
Table 4. 2 Dimensions of the seven pole OSKLR ...................................................................................................... 38
Table 4. 3 Dimensions of the three pole OLSR .......................................................................................................... 42
Table 4. 4 Comparison between the three filters ......................................................................................................... 44
Table 5. 1 Dimensions of the compact UWB filter ..................................................................................................... 47
1
CHAPTER ONE
Introduction
In the previous years, wireless communication systems has developed tremendously, there was
a prompt development in ultra-wideband systems, wireless internet like Wifi and Wimax,
broadband personal communication systems and 3G (third generation), 4G (fourth generation)
technologies. Due to this rapid development there was a need for more rigid microwave
components. And now a days satellite systems changed their path from static telecommunications
systems to mobile, remote sensing and navigation applications. Microwave components plays an
important role in the satellite systems. Microwave components include microwave resonant
components such as microwave filters, dielectric resonant antenna arrays (DRA), duplexers.
Because of the rapid growth in the wireless communication area, it created more challenging
requirements that enforce challenges on various novel designs, optimization and understanding of
components. In microwave filters the challenges are to be faced in miniaturization, bandwidth,
phase linearity, and selectivity of the filters.
1.1 Microwave Communication:
The electromagnetic waves are the waves whose frequency ranges from 300 MHz - 300 GHz,
these range of frequencies are referred as microwaves. The wavelength of this waves in free space
is about 1 m – 1 mm. The electromagnetic spectrum is shown in figure 1.1, it demonstrates
schematically the electromagnetic spectrum. Further some selected frequency spectrums are
allocated into many frequency bands as betokened in Table 1.1. Frequency boundaries between
RF and microwave are almost arbitrary. The boundary rely on the specific technologies established
2
for the utilization of that particular frequency range. The applications that use RF/microwave
frequency ranges are communications, remote sensing and many more.
Figure 1. 1 Electromagnetic spectrum
Frequency range Band designation
140-220 GHz G-band
110-170 GHz D-band
75-110 GHz W-band
60-90 GHz E-band
50-70 GHz V-band
40-60 GHz U-band
3
33-50 GHz Q-band
26.5-40 GHz Ka-band
18-26.5 GHz K-band
12.4-18GHz Ku-band
8-12.4 GHz X-band
4-8 GHz C-band
2-4 GHz S-band
1-2 GHz L-band
500-1000 MHz UHF-band
50-500 MHz VHF-band
Table 1.1 Frequency bands
1.2 Definition of a Filter
A filter is used to regulate the frequency response at a fixed point in the EM spectrum by providing
low loss transmission at the preferred frequency band and high attenuation at remaining
frequencies. Filters are extensively used in many applications like communications, remote
sensing, radars etc. A filter is generally a two-port network.
4
1.3 Role of filters in microwave communication
Filters are essential in separating and sorting signals in communication systems. To cull or confine
the RF/microwave signals within given spectral limits, filters are used. The role of filters in
communication systems is to usually transmit and receive amplitude and/or phase modulated
signals through a communication channel. To get rid of or suppress spurious frequencies from
being transmitted or received in radio transmitters and receivers, filters are used. Evolving
applications such as wireless communication remains to challenge RF/microwave filters with even
more rigid requirements like smaller size, lighter weight and lower cost with better performance.
Filters used in communication and radar applications, are implemented in different kinds of
transmission lines comprising stripline, rectangular waveguide, and microstrip. Filters are also the
integral part of multiplexers which are of major demand in the broadband wireless access
communication systems.
1.4 Applications of filters
Microwave filters play an important role in almost every RF/microwave communications system.
A microwave filter is basically a device that is used to discriminate between wanted and unwanted
signals within a specified frequency band. The term microwave refers to the frequency range
between 300 MHz and 30 GHz. As the communication systems evolve, higher frequencies are
explored and new standards are set. Also, the filter requirements in terms of selectivity become
more stringent due to the limited available frequency spectrum. Other filter specifications are
generally dictated by the intended application. Examples of filter characteristics and applications
will be presented in the next section.
5
1.5 Satellite filters
Satellite filters cover a large frequency range depending on the specific service offered by the
satellite payload [1]. For example, navigation mobile satellite systems are naturally activated in
the L and S bands (1-2 GHz, 2-4 GHz, respectively) and remote sensing applications will work
mainly in the C band (4-8 GHz). For most viable communications, there is an outstanding high
demand on the frequency spectrum, higher Ku band (12-18 GHz) and other upper frequency bands
(20-30 GHz) are considered [2]. A communication satellite is basically a repeater that receives
microwave signals, amplifies them and resends them to the receiving end. The bandwidth is
divided into narrow band channels, since the practical considerations due to non linearities and
effect of noise in power amplifiers. The partition and recombination of channels are done by means
of input and output multiplexers individually. The input and output multiplexers are poised of
many narrow bandpass filters (typical fractional bandwidths between 0.2% and 2%). Satellite
microwave bandpass filters have been typically executed using waveguide technology due to high
quality factors and high power handling capability. On the other hand, waveguide filters are bulky
and heavy. There has been a significant amount of work done to reduce the size and weight of
satellite filters. A fruitful solution involves using dual-mode cavities, i.e. cavities that support two
degenerate resonances [5-7]. This reduces the amount of physical cavities by an aspect of two.
Also, the usage of dual-mode cavities permits the implementation of topologies that are capable
of producing transmission zeros at finite frequencies and hence improving filter selectivity.
1.6 Microwave filters in cellular communication
Microwave filters are very important components in cellular systems where stringent filter
specifications are required both on the mobile station and base station levels. All modern full
6
duplex personal communications systems require transmit and receive filters for each transceiver
unit at least at the base station level. Transmit filters must be very selective to prevent out of band
inter-modulation interference to satisfy regulatory requirements as well as prevent adjacent
channel interference. Acceptable levels of adjacent channel interference in TDMA second
generation mobiles are specified in GSM ETSI standards as C/A > -9dB. In practice a C/A of -6
dB is used in the network design. Also, the transmit filters must have low insertion loss to satisfy
efficiency requirements. A typical transmit filter contains a return loss of 20dB and passband
insertion loss of 0.8 dB. It is obvious that the technology used in filter realization in base stations
is significantly different from that used in handsets. Although the filter specifications in handsets
are less stringent due to lower power handling (33dBm maximum transmit power), size
requirements remain a challenging task. One of the main difficulties is parasitic or unwanted
coupling that is caused by the close proximity of the resonators.
Another application of filters is in cellular systems microwave links to connect base stations to
BSC (base station controller) and then to the MSC (Mobile Switching Center). These are high-
speed links with directive dish antennas. There are few licensed bands for transmission such as 8,
11, 18, 23, 24 and 38 GHz. The choice of the frequency band depends on spectrum availability,
length of the hop and required link reliability. Filters for transmission systems are usually
constructed using waveguide technology due to the high quality factors requirements and high
power handling capabilities.
1.7 Literature review on Microwave filters
Despite the extensive literature in the field of microwave filters, several issues are still either not
well understood or lack a systematic solution or accurate design procedure. For instance, one of
the major difficulties with miniaturized and compact filters is parasitic coupling that can be in the
7
order of the main coupling in compact filters. This makes it difficult to identify a sparse topology
on which most of design and optimization methods are based. It is sometimes impossible to predict
the behavior of the filter when using a conventional coupling topology based on the arrangement
of physical resonators. Most importantly, the absence of a reliable circuit model that represents
compact filters makes the optimization of this class of filters, within efficient and systematic
techniques such as space mapping technique, impossible. The same argument holds for wideband
filters that cannot be represented by the conventional low-pass prototypes that are based on a
narrowband approximation.
One of the major difficulties with microwave filter design is the absence of a generic design
technique to transform the low-pass prototype into physical dimensions except for few cases as in
[5, 6]. A careful investigation of the available literature reveals that this is due to basing most of
the design techniques unswervingly on the phenomenon of resonance. The dependence of the
resonant frequencies of the resonators on the coupling strength (loading) is not systematically
accounted for in the model. It is indeed shown that by using the phenomenon of propagation
instead of resonance, it becomes straightforward to account for the piling of the resonances by the
coupling components as in in-line direct-coupled resonator filters [3].
Despite the widespread use of dual-mode filters in satellite communications, the design and
realization of this class of filters is not straightforward. The concept of dual-mode filters was
anticipated by Atia and Williams in the 1970’s [5-7]. In general, filters designed according to this
theory require extensive optimization. Tuning elements are used as part of the CAD design as well
as in compensating for inherent manufacturing errors. The resulting designs are very time-
consuming, labor intensive, costly and at times extremely sensitive. A satisfactory solution to this
problem is not known.
8
The main goal of this thesis is to find new techniques for the design of bandpass microstrip filters.
Detailed investigation of the relevance of equivalent circuits used to represent the filter response
to the field theory is carried out in detail. The new view is exploited to formulate new design and
implementation methods for microwave filters.
1.8 Organization of Thesis
The organization of thesis is as follows:
Chapter one gives a brief overview about microwave communication, microwave filters and its
applications, and literature review on microwave filters.
Chapter two is dedicated to the basic concepts of transmission lines, the discussion is strictly
limited to the concepts which are helpful only in designing microstrip filters.
Chapter three gives a brief introduction to the types of microstrip filters and their applications.
In Chapter four, novel techniques which are used in designing the bandpass filters are presented.
The novel designs includes OSKLRs and OSSLRs. The simulated designs and results are
presented.
In Chapter five, a new type of MMR is discussed, which is implemented in designing the UWB
filter.
The simulated results of the UWB filter are presented in detail.
In Chapter six, general conclusion and suggestion for future work is presented.
9
CHAPTER TWO
Basic concepts of Transmission Lines
The essential theories and the equations which are helpful in designing the microstrip lines,
discontinuities, components compatible for filter design, and coupled microstrip lines are concisely
explained.
2.1 Microstrip Lines
2.1.1 Structure of the Microstrip
The common structure of a microstrip is demonstrated in Figure 2.1. A microstrip line of thickness
t and width W sits on the top of a dielectric substrate. The dielectric substrate of thickness h has a
relative dielectric constant εr, and there is a ground plane at the bottom of the structure.
2.1.2 Waves in Microstrip
The microstrip structure is inhomogeneous because the fields arising from the corners is exhibited
into two media, “air above and dielectric below”. The microstrip will not be able to back a perfect
TEM wave because of this inhomogeneous nature. This is due to that a perfect TEM wave has
only transverse electric and magnetic field components whose propagation velocity is a function
of the material parameters like permittivity ε and the permeability µ. However, the waves in a
microstrip line does not possess longitudinal components of EM fields because of the presence of
the dielectric substrate and the air which are called as two guided-wave media.
10
Figure 2. 1 Broad microstrip structure
2.1.3 Quasi-TEM Approximation
The longitudinal components may be neglected when the fields in the dominant mode of a
microstrip line. These fields remain very much negligible than the transverse electric and magnetic
components. In this instance, the dominant mode will be behaving like a TEM mode, therefore the
transmission line theory for TEM mode can also be applicable for the microstrip line. This
approximation is valid for most of the operating frequencies of the microstrip.
11
2.1.4 Guided Wavelength, Propagation Constant, Phase Velocity, and
Electrical Length
The guided wavelength of the quasi-TEM mode is
λg =
λ0√εre
(2.1)
Here, 𝜆0 = free space wavelength. For the convenience, frequency is specified in gigahertz (GHz),
and the guided wavelength in millimeters as monitors:
𝜆𝑔 = 300
𝑓(𝐺𝐻𝑧)√𝜀𝑟𝑒 𝑚𝑚 (2.2)
The allied propagation constant 𝛽 related to guided wavelength 𝜆𝑔 and phase velocity vp can be
given by:
𝛽 = 2𝜋
𝜆𝑔 (2.3)
𝑣𝑝 = 𝜔
𝛽 =
𝑐
√𝜀𝑟𝑒 (2.4)
where
c ≈ 3.0 × 108 m/s
The electrical length of the microstrip can be given by,
𝜃 = 𝛽𝑙 (2.5)
Henceforth, θ = π/2 when l = λg/4, and θ = π when l = λg /2. In designing the microstrip filters
these two important parameters half-wavelength (λg /2) and quarter-wavelength (λg/4) microstrip
lines are very essential.
12
2.1.5 Dispersion in Microstrip
In common the microstrip dispersions; viz., its phase velocity is not a constant factor but varies
according to the operating frequency. The effective dielectric constant εre depends on the operating
frequency. As the frequency of operation increases the value of effective dielectric constant
reaches towards the actual value of dielectric constant. To consider the dispersion effect, the
effective dielectric constant can be expressed as a function of frequency. Which can be given by
the expression:
ε𝑟𝑒(𝑓) = ε𝑟 −ε𝑟−ε𝑟𝑒
1+(𝑓
𝑓50)
𝑚 (2.6)
where
𝑓50 = 𝑓𝑇𝑀0
0.75+(0.75−0.332ε𝑟−1.73)𝑊/ℎ
(2.7)
𝑓𝑇𝑀0=
𝑐
2𝜋ℎ√(ε𝑟−ε𝑟𝑒)𝑡𝑎𝑛−1 (ε𝑟√
ε𝑟𝑒−1
ε𝑟−ε𝑟𝑒) (2.8)
𝑚 = 𝑚0𝑚𝑐 ≤ 2.32 (2.9)
𝑚0 = 1 +1
1+√(𝑊
ℎ)
+ 0.32 (1
1+√(𝑊
ℎ))
3
(2.10)
𝑚𝑐 = 1 +1.4
1+𝑊
ℎ
0.15 − 0.235𝑒𝑥𝑝 (−0.45𝑓
𝑓50) 𝐹𝑜𝑟
𝑊
ℎ≤ 0.7 (2.11)
𝑎𝑛𝑑
1 𝐹𝑜𝑟𝑊
ℎ≥ 0.7
The dispersion also effects the characteristic impedance, which is given by
13
𝑍𝑐 = 𝑍𝑐ε𝑟𝑒(𝑓)−1
ε𝑟𝑒−1√
ε𝑟𝑒
ε𝑟𝑒(𝑓) (2.12)
where
𝑍𝑐 − Quasistatic value of characteristic impedance
2.1.6 Losses in Microstrip
The radiation losses, conductors, and dielectrics, magnetic substrates (here the magnetic loss plays
a role, like as ferrites) are the lossy components. The propagation constant is complex on the lossy
transmission line; viz.,𝛾 = 𝛼 + 𝑗𝛽, where the attenuation constant is denoted by α which is the real
part and the unit of α is nepers per unit length and is expressed in decibels dB/unit length, it is
shown as
𝛼(𝑑𝐵 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ⁄ ) = (20𝑙𝑜𝑔10𝑒)𝛼(𝑛𝑒𝑝𝑒𝑟𝑠 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ)⁄
≈ 8.686𝛼(𝑛𝑒𝑝𝑒𝑟𝑠 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ)⁄
2.1.7 Enclosure Effect
Most of the microstrip circuits uses a metallic enclosure, for example filters. The metallic
conducting walls effects the characteristic impedance and the ε𝑟𝑒. To overcome this enclosure
effect, the height is taken eight times more than the height of the substrate and the distance from
the walls is taken five times more than the height of the substrate.
14
2.1.8 Higher order modes and Surface Waves
By operating below the cutoff frequency of the dominant higher order mode, we can sidestep the
excitation of the higher order modes. The cutoff frequency of the dominant higher order mode can
be expressed as:
𝑓𝑐 =𝑐
√𝜀𝑟 (2𝑊+0.8ℎ) (2.13)
Surface wave generates in the air dielectric interface on a metallic ground plane. The frequency
related to surface wave mode can be given by:
𝑓𝑠 =𝑐 𝑡𝑎𝑛−1𝜀𝑟
√2𝜋ℎ√𝜀𝑟−1 (2.14)
2.2 Coupled microstrip lines
For implementing microstrip filters coupled microstrip lines are extensively used. A pair of
coupled microstrip lines is described in Figure 2.2, they are in edge coupled configuration in which
a pair of microstrip lines are of width w and separated by a distance s. This configuration generates
two quasi -TEM modes, which are the even and odd modes shown in Figure 2.3.
Figure 2. 2 Cross sectional view of the pair of coupled microstrip lines
15
Figure 2. 3 Quasi-TEM modes of a coupled microstrip lines pair
Even mode:
In this mode, both microstrip lines carry the similar charges which are the positive ones or does
have the same voltage potentials, due to this magnetic wall is formed at the symmetry plane, as
illustrated in Figure 2.3(a).
Odd mode:
In this mode, both microstrip lines carry the charges with the opposite signs or does have the
opposite voltage potentials, due to this electric wall is formed at the symmetry plane, as shown in
Figure 4.3(b).
In the same time these two modes will be excited in common. As they are not pure TEM modes
they have different phase velocities and different permittivities. Henceforth, these lines are
categorized by the effective dielectric constants and the characteristic impedances for both the
modes [23].
16
2.2.1 Design Equations
The characteristic impedances and the effective dielectric constants are given below. The
expression for static approximation (dispersion is not considered) is expressed by:
𝜀𝑒𝑟𝑒 =
𝜀𝑟+1
2+
𝜀𝑟−1
2(1 +
10
𝑣)
−𝑎𝑒𝑏𝑒
(2.15)
with
𝑣 = 𝑢(20+𝑔2)
10+𝑔2 + 𝑔 exp(−𝑔) (2.16)
𝑎𝑒 = 1 +1
49𝑙𝑛 [
𝑣4+(𝑣 52)2⁄
𝑣4+0.432] +
1
18.7𝑙𝑛 [1 + (
𝑣
18.1)3] (2.17)
𝑏𝑒 = 0.564 (𝜀𝑟−0.9
𝜀𝑟+3)
0.053
(2.18)
where 𝑢 = 𝑊/ℎ and 𝑔 = 𝑠 ℎ⁄ . The error in 𝜀𝑒𝑟𝑒 is within 0.7% over the ranges of 0.1 ≤ 𝑢 ≤
10, 0.1 ≤ 𝑔 ≤ 10, and 1 ≤ 𝜀𝑟 ≤ 18.
𝜀0𝑟𝑒 = 𝜀𝑟𝑒 + [0.5(𝜀𝑟 + 1) − 𝜀𝑟𝑒 + 𝑎0] exp (−𝑐0𝑔𝑑0) (2.19)
with
𝑎0 = 0.7287[𝜀𝑟𝑒 − 0.5(𝜀𝑟 + 1)] [1 − exp(−0.17𝑢)] (2.20)
𝑏0 =0.747𝜀𝑟
0.15+𝜀𝑟 (2.21)
𝑐0 = 𝑏0 − (𝑏0 − 0.207) exp(−0.414𝑢) (2.22)
𝑑0 = 0.593 + 0.694 exp (−0.562𝑢) (2.23)
where
𝜀𝑟𝑒 − Static effective dielectric constant of single microstrip of width W
The error in 𝜀0𝑟𝑒 is of the order of 0.5%.
𝑍𝑐𝑒 = 𝑍𝑐√𝜀𝑟𝑒 𝜀𝑒
𝑟𝑒⁄
1−𝑄4√𝜀𝑟𝑒 . 𝑍𝑐/377 (2.24)
17
where 𝑍𝑐 − Characteristic impedance of single microstrip of width W
𝑄1 = 0.8695𝑢0.194 (2.25)
𝑄2 = 1 + 0.7519𝑔 + 0.189𝑔2.31 (2.26)
𝑄3 = 0.1975 + [16.6 + (8.4
𝑔)6]
−0.387
+1
241ln [
𝑔10
1+(𝑔
3.4)10
] (2.27)
𝑄4 =2𝑄1
𝑄2
1
𝑢𝑄3 exp(−𝑔)+[2−exp(−𝑔)]𝑢−𝑄3 (2.28)
𝑍𝑐𝑜 = 𝑍𝑐√𝜀𝑟𝑒 𝜀0
𝑟𝑒⁄
1−𝑄10√𝜀𝑟𝑒 𝑍𝑐/377 (2.29)
with
𝑄5 = 1.794 + 1.14 𝑙𝑛 [1 +0.638
𝑔+0.517𝑔2.43] (2.30)
𝑄6 = 0.2305 +1
281.3ln [
𝑔10
1+(𝑔
5.8)10
] +1
5.1 ln (1 + 0.598𝑔1.154) (2.31)
𝑄7 =10+190𝑔2
1+82.3𝑔3 (2.32)
𝑄8 = 𝑒𝑥𝑝 [−6.5 − 0.95 ln(𝑔) − (𝑔
0.15)5] (2.33)
𝑄9 = ln(𝑄7) (𝑄8 + 1 16.5⁄ ) (2.44)
𝑄10 = 𝑄4 −𝑄5
𝑄2𝑒𝑥𝑝 [
𝑄6 ln (𝑢)
𝑢𝑄9] (2.45)
18
These closed-form expressions are also used to obtain precise values of capacitances for even and
odd modes. The formulations of the effect of dispersion are found in above derived equations.
2.3 Discontinuities in Microstrip
Discontinuities in microstrip would frequently come across in the practical filter structures which
comprises open-ends, gaps, steps, junctions, and bends. Fig 2.4 shows certain distinctive layouts
and layout equivalent circuits. Full wave EM simulations can be used to model the filter designs
by considering the discontinuities.
19
Figure 2. 4 Discontinuities in microstrip
2.4 Microstrip Components
Microstrip components are also taken into account to design the filters. They may have lumped
and quasi lumped components, and resonators. These components are illustrated in Figures 2.5
and 2.6. The size of this components as compared to the free space wavelength are much smaller.
Because this compact size they can easily manufacture by monolithic microwave integrated
circuits.
20
Figure 2. 5 Lumped-element inductors
21
Figure 2. 6 Lumped-element capacitors
2.5 Resonators
A structure which is able to enclose at least one oscillating electromagnetic field is called a
Microstrip resonator. There are various forms of microstrip resonators. Microstrip resonators for
filter designs may be classified as quasi lumped-element resonators or lumped-element and
distributed line or patch resonators. Some classic configurations of these resonators are illustrated
in Figure 2.7.
22
Figure 2. 7 Some typical microstrip resonators
23
CHAPTER THREE
Types of Microstrip Filters and Their
Applications
3.1 Lowpass and Bandpass Filters
Orthodox microstrip lowpass and bandpass filters such as pseudo-combline filters , stepped-
impedance filters, semi-lumped element filters, open-stub filters, end- and parallel-coupled half-
wavelength resonator filters, hairpin-line filters, interdigital and combline filters, and stub-line
filters, are extensively used in various RF/microwave applications. Different types of lowpass and
bandpass filters are listed below:
3.1.1 Lowpass Filters
There are two main steps in the design of microstrip lowpass filters. The initial one is to select a
suitable lowpass model. The type of response, comprising and the number of reactive elements
and passband ripple, will be determined by the required specifications. The lowpass filters are
designed approximately in three types, they are:
Stepped-impedance L-C ladder-type lowpass filters
L-C ladder type of lowpass filters using Open-circuited stubs
Semi-lumped lowpass filters having Finite-Frequency Attenuation Poles
3.1.2 Bandpass Filters
The Bandpass filters are designed approximately in seven types, they are:
End-Coupled, Half-Wavelength Resonator Filters
24
Parallel-Coupled, Half-Wavelength Resonator Filters
Hairpin-Line Bandpass Filters
Interdigital Bandpass Filters
Combline Filters
Pseudocombline Filters
Stub Bandpass Filters
Filters with 𝜆𝑔0/4 Short-circuited Stubs
Filters with 𝜆𝑔0/2 Open-circuited Stubs
3.2 Highpass and Bandstop Filters
There are different types of microstrip Highpass and Bandstop filters are present including,
narrow-band and wide-band bandstop filters, quasilumped element and optimum distributed
highpass filters, as well as filters used for RF chokes. Different types of highpass and bandstop
filters are listed below:
3.2.1 Highpass Filters
The Highpass filters are designed approximately in two ways, they are:
Quasilumped Highpass Filters
Optimum Distributed Highpass Filters
3.2.2 Bandstop Filters
The Bandstop filters are designed approximately in four ways, they are:
Narrow-Band Bandstop Filters
Bandstop Filters with Open-Circuited Stubs
Optimum Bandstop Filters
25
Bandstop Filters for RF Chokes
3.3 Coupled-Resonator Circuits
Coupled resonator circuit’s plays a vital role in the design of RF/microwave filters, mainly in the
narrow-band bandpass filters which plays a key role in many microwave applications. Despite of
any type of physical structure, there is a common technique which can be used for designing
coupled resonator filters. The technique has been applied to the design of dielectric resonator
filters, waveguide filters, microstrip filters, ceramic combline filters, micromachined filters, and
superconducting filters. This design based on coupling coefficients of intercoupled resonators and
the external quality factors of the input and output resonators. As this design is so useful and
flexible, it can be used in designing many types of coupled resonator circuits.
3.4 Filter Miniaturization and Compact Filters
When compared to wave guide filters microstrip filters are very small in size. Nonetheless, there
are some applications where the miniaturization is of primary importance, so smaller microstrip
filters are required. If the size is reduced then it leads to increase in the dissipation losses in a given
material and hence it tends to reduction in the performance. Even though this demerit doesn’t
shows much effect on the miniaturization of the filters. Reduction of size in filters may be achieved
by using high dielectric constant substrates or lumped elements, but very regularly for specified
substrates, a change in the geometry of filters is required and as a result various new filter structures
can be achieved. There are many new types of filters include ladder line filters, slow-wave
resonator filters, compact open-loop and hairpin resonator filters, pseudointerdigital line filters,
miniaturized dual-mode filters, multilayer filters, filters using high dielectric constant substrates
and lumped-element filters.
26
3.5 Ultra-Wideband Filters
There are many emerging applications which are using ultra-wide band frequency range. For these
emerging applications UWB or broad-band microwave filters are essential components. The
applications include UWB wireless and radar systems also. Due to this rapid growth, it has
stimulated the development of various types of UWB filters which includes short-circuit stubs,
those using coupled single or multimode resonators, or quasilumped elements, those based on
cascaded high-and-lowpass filters, and those with single or multiple notched bands.
3.6 Electronically Tunable and Reconfigurable Filters
Electronically tunable or reconfigurable filters are becoming more and more popular in the field
of research developments, because of their growing significance in improving the capability of
current and future wireless systems. Electronically reconfigurable microwave filters will be
playing a vital role in the future cognitive radio and radar applications.
In common, to develop an electronically or reconfigurable filter, active switching or tuning
elements such as semiconductor p-i-n and varactor diodes, RF MEMS, or other functional material
based components including ferroelectric varactors need to be integrated within a passive filtering
structure. Since microstrip filters can conveniently integrate this kind of small sizes, there has been
significant development in the tunable or reconfigurable microstrip filters. These filters are
classified into:
Tunable combline bandpass filters
RF MEMS tunable filters
Piezoelectric transducer (PET) tunable filters
Tunable high-temperature superconductor (HTS) filters
27
Reconfigurable UWB filters
Tunable dual-band filters
Tunable Bandstop filters
Reconfigurable/tunable dual-mode filters
Reconfigurable bandpass filters based on switched delay-line approach
Wideband bandpass filter with reconfigurable bandwidth
In general, bandwidth tuning or controlling is more difficult than frequency tuning and the
design of an electronically tunable filter with a wider bandwidth is more difficult than a narrow
bandwidth in terms of bandwidth control and tuning range.
3.7 Advanced RF/Microwave Filters
To meet the stringent requirements from RF/microwave systems (specifically from the wireless
communication systems) there has been urging demand for advanced RF/microwave filters other
than conventional chebyshev filters. The different types of advanced RF/microwave filters are
listed below:
Selective filters with a single pair of transmission zeroes
Cascaded quadruplet (CQ) filters
Trisection and cascaded trisection (CT) filters
Transmission line inserted filters
Linear-phase filters
Extracted pole filters
Canonical filters
Multiband filters
28
3.8 High-Temperature Superconducting (HTS) filters
High-temperature superconductors are discovered in 1986, since the discovery high-temperature
super conductivity has been at the pole position of advanced filter technologies and has changed
the way of designing communication systems, namely medical instrumentation, electronic
systems, military microwave systems, satellite communication systems, mobile communication
systems, and radio astronomy and radars. Most of the superconducting filters are simply microstrip
structures using HTS thin films. The development of HTS thin films and the fabrication of HTS
microstrip filters are compatible with hybrid and monolithic microwave-integrated circuits. The
most commercially available HTS materials are
1. Yttrium barium copper oxide (YBCO) - [YBa2Cu3O7-x, 𝑇𝑐(𝑘) ≈ 92]
2. Thallium barium calcium copper oxide (TBCCO) – [Tl2Ba2Ca1Cu2Ox, 𝑇𝑐(𝑘) ≈ 105 ]
Where 𝑇𝑐(𝑘) is the typical Transition temperature.
29
CHAPTER FOUR
Design of Bandpass filters Using Open split
Resonators
Microstrip bandpass filters are used to cull or combine the RF/microwave signals within certain
spectral boundaries within the electromagnetic spectrum. Dual mode resonator usage allows to
realize the compact high quality of bandpass filter (BPF). There are two filters in this chapter
which are designed using the fractal geometry and a filter which is designed on the base of square
loop resonator, these filters are having a very low insertion loss which is less than -1db, reduced
return loss and good pass band performance. This chapter is dedicated to the design of bandpass
filters using novel open split resonators like Open split koch loop resonator’s (OSKLR’s) and open
loop square resonators are designed. First a three pole compact Koch resonator is designed on a
ptfe substrate and it is followed by the design of semi lumped bandpass filter using open split Koch
resonator and a three pole element compact open loop square resonator.
4.1 Introduction
With the invention of new materials and innovative fabrication techniques, Microstrip filters are
being extensively used in various microwave applications due to their high performance, small
size and low cost. Microstrip band pass filters can be designed with the help of many topologies
like end-coupled, half-wavelength resonator filters, parallel-coupled, half-wavelength resonator
filters, hairpin-line bandpass Filters, interdigital bandpass filters, combline filters, pseudocombline
filters, stub bandpass filters. Because of the relatively weak [9] coupling microstrip coupled line
filters has been used to attain narrow bandwidth bandpass filters. This type of filters has many
30
advantages like easy integration and low cost fabrication. The dual mode resonators helps in
realizing compact high quality microwave bandpass filters [10].
Dual mode microstrip filters are generally in the form of a square, ring or a disk patch. Normally
these square, ring or a disk patches are referred to as dual mode resonators. Due to the difficulty
in the modes of coupling the two different rings make the circular ring resonators not practical for
designing higher order filters [11]. The square ring resonator has the simple and strong coupling
between two individual resonators. Nevertheless the degenerate modes are still coupled by a
perturbation at more than one corners. Use of koch loop resonators doesn’t require this
perturbations and modest coupling between all the modes is possible. The advantages of koch loop
resonator is it has a smaller size than a normal koch patch [9] and resonant frequencies being
controlled by changing the dimensions of the loop.
The backbone of fractal geometry is its recursive generating methodology which outlines with
many complicated structures. Numerous fractal geometries like Koch curve, Hilbert curve,
Sierpinski gasket, etc. have been studied extensively to improve numerous microwave devices
[12], like microstrip bandpass filters, antennas etc.,. All these fractals have the advantage of
miniaturization, multi-band, wide-band operation. The two basic properties of fractals are space
filling ability and self-similarity. Here, space filling defines that a fractal shape can me filled in a
finite region without increasing the whole area. Self-similarity defines that a part of the fractal
geometry will always reflects the entire structure. The filters designed with fractal geometry are
having reduced return loss and good passband performance.
31
4.2 Koch curve
The Koch curve is an example of fractal geometry. The features of Koch fractal geometry has been
applied to various applications such as miniaturization of conventional antennas [13], ultra wide
band filters [14], coupled -line bandpass filters [15], etc. To construct a Koch curve, a straight line
should be divided into three parts which should be in equal size. Now, the section which is in the
middle is replaced with an equilateral triangle by removing its base. The length is augmented by a
factor of 4/3 after the first iteration. As these iterations will be repeated, the total length of the
figure will become infinity and because of this the lengths of the new triangle moves to zero.
Figure shows the fractal Koch curve structure. The one of the predominant features of the koch
curve is, it can accommodate infinite length in a finite region.
Figure 4. 1 Koch curve
32
4.3 Filter designs
4.3.1 A Three pole Open Split Koch Loop Resonator (OSKLR)
Open split koch loop resonators are used in these designs to design bandpass filters. These type of
resonators works as lumped LC series elements because of their very small electrical size [16].
These can be used as building blocks of small size bandpass filters [17]. The capacitance and the
inductance values can be regulated by altering the geometrical parameters of the coupled rings.
This filter configuration has typically contains three OSKLRs, interconnected with a microstrip
line. The patch sits on a Polytetrafluoroethylene (PTFE) substrate which is of thickness 0.49 mm
and permittivity εr = 2.43. The filter has been modeled using the optimization code used in [18].
Here, the filter bandwidth can be regulated by altering the length of the unit cell, d, and the rejection
band depth is based on the number of transmission poles, N, used for implementing the filter [25].
The structure of the filter is shown in the following figures 4.2, 4.3, and the s-parameter is shown
in figure 4.4.
Figure 4. 2 Open Split Koch Loop Resonator
33
(a) Front view
(b) Ground plane view
Figure 4. 3 Design and dimensions of the simulated five pole OSKLR slow-wave filter
34
Figure 4. 4 S-Parameter of the designed filter
Dimensions of the filter
Parameters Value
External koch radius 2.2 mm
Koch ring width 0.14 mm
Slot between the two koch rings 0.25 mm
Height of the PEC 0.05 mm
Length of the substrate 15 mm
Width of the substrate 40 mm
Height of the substrate 0.49 mm
Substrate material PTFE, εr = 2.43
Table 4. 1 Dimensions of the three pole OSKLR
35
Simulated Results
The objective of the resonant frequency was about 3-4 GHz. The 50Ω length microstrip sections
between OSKLRs produced a bandwidth of 28%. The design of the filter is shown in Figure 4.3.
Here the filter is shortened by connecting the meander transmission lines to the OSKLRs. The S-
Parameter result of the designed filter is shown in figure 4.4. The filter is simulated in a full-wave
electromagnetic simulation in CST Microwave studio.
36
4.3.2 Seven pole Open Split Koch Loop Resonator (OSKLR)
This filter configuration has typically contains seven OSKLRs interconnected with a microstrip
line. The patch sits on a RT/Duroid substrate which is of thickness 0.254 mm and permittivity εr
= 10.2. The central frequency of this bandpass filter is 𝑓0 = 5 𝐺𝐻𝑧. The structure of the filter is
shown in the following figures 4.5, 4.6, and the s-parameter is shown in figure 4.7. A filter of
order N = 7 is selected in order to attain good rejection band in outer band region. The geometry
of the strip width and transmission line is taken from quasi-TEM code presented in [16].
Figure 4. 5 OSKLR
37
(a) Front view
(a) Ground plane view
Figure 4. 6 Design and dimensions of the filter
38
Figure 4. 7 S-Parameter of the designed filter
Dimensions of the filter
Parameters Value
External koch radius ( Rext ) 1.101 mm
Koch ring width (c) 0.2 mm
Slot between the two koch rings (d) 0.2 mm
Height of the PEC 0.05 mm
Length of the substrate 41.4 mm
Width of the substrate 5.2 mm
Height of the substrate 0.254 mm
Substrate material RT/Duroid, εr = 10.2
Table 4. 2 Dimensions of the seven pole OSKLR
39
Simulated Results
The final design and the results are shown in figures, comparing this results with measurements
the central frequency of the filter (5 GHz) has been attained. This filter produced a bandwidth of
14%. The rejection curve at the both sides of the passband looks balanced. Here the filter is
shortened by connecting the meander transmission lines to the OSKLRs. The S-Parameter result
of the designed filter is shown in figure 4.7. The filter is simulated by a full-wave electromagnetic
simulation in CST Microwave studio.
40
4.3.3 Three Pole Element Compact Open Loop Square
Resonator
In this design a new type of open loop square resonator is implemented [20]. The proposed filter
configuration has typically contains three OLSRs and a Polytetrafluoroethylene (PTFE) substrate
is used which is of thickness 0.49 mm and permittivity εr = 2.43. The filter has been modeled using
the optimization code used in [18]. The structure of the filter is shown in the following figures
4.2, 4.3, and the s-parameter is shown in figure 4.4.
Figure 4. 8 Open Loop Square Resonator
41
(a) Front view
(a) Ground plane view
Figure 4. 9 Design and dimensions of the simulated three pole OLSR filter
42
Figure 4. 10 S-Parameter of the designed filter
Dimensions of the filter
Parameters Value
Length of the square 2.2 mm
Square loop width 0.14 mm
Slot between the two square loop 0.25 mm
Height of the PEC 0.05 mm
Length of the substrate 15 mm
Width of the substrate 40 mm
Height of the substrate 0.49 mm
Substrate material PTFE, εr = 2.43
Table 4. 3 Dimensions of the three pole OLSR
43
Simulated Results
This filter has produced a bandwidth of 0.46%. The design of the filter is shown in Figure 4.9 and
the s-parameter is shown in 4.10. Here the filter is shortened by connecting the meander
transmission lines to the OLSRs. The S-Parameter result of the designed filter is shown in figure
4.4. The filter is simulated in a full-wave electromagnetic simulation in CST Microwave studio.
4.4 Conclusion
Design 1
A New Five Pole Open Split Koch Loop Resonator, has been designed and investigated. The
desired bandwidth of 28% has been achieved. This resonator can be useful in the design of compact
bandpass filters in microstrip technologies. The three pole bandpass filter has been designed on
the basis of microstrip technology, the filter has been designed and simulated. Particularly simple
circuit model is used in the design of this filter, where the circuit parameters are in quasi-analytical
form. The bandwidth is tuned by the length of the line sections sandwiched between the OSKLRs.
The results of the theoretical predictions and full-wave simulations are apparently matched and the
results are upright at a comprehensive frequency range around the filter and passband.
Design 2
A bandpass filter has been designed and executed by using OSKLRs. In this design λ/4 inverters
has been used with altered characteristic impedances joining the indistinguishable OSKLRs. The
desired bandwidth of 14% has been achieved. The results of the theoretical predictions and full-
wave simulations are apparently matched and the results are upright at a comprehensive frequency
range around the filter and passband.
44
Design 3
A New Two pole Open Loop Square Resonator, has been designed and investigated. The desired
bandwidth of 0.46% has been achieved. This resonator can be useful in the design of compact
bandpass filters in microstrip technologies. The two pole bandpass filter has been designed on the
basis of microstrip technology, the filter has been designed and simulated. Particularly simple
circuit model is used in the design of this filter, where the circuit parameters are in quasi-analytical
form. The position of first pole in this design tends to the OLSRs resonance frequency, and the
bandwidth is tuned by the length of the line sections sandwiched between the OLSRs. The results
of the theoretical predictions and full-wave simulations are apparently matched and the results are
upright at a comprehensive frequency range around the filter and passband.
4.5 Comparison between the three filters
Filters Bandwidth Dimensions Substrate
3 Pole Koch Resonator 28% 40 X 15 mm2 PTFE
7 Pole Koch Resonator 14% 41.4 X 5.2
mm2
RT/Duroid
RO 3210
3 Pole Square Loop Resonator 0.46% 40 X 15 mm2 PTFE
Table 4. 4 Comparison between the three filters
45
CHAPTER FIVE
Compact UWB Star Shaped Multiple-Mode
Resonator for Bandpass Filter with
Enhanced Upper-Stopband Performance
5.1 Introduction
In 2002 the U.S. Federal Communications Committee (FCC) released the unlicensed use of ultra-
wideband (UWB) frequency spectrum for indoor and hand-held wireless communications. After
that there has been a remarkable interest in investigation of variety of bandpass filters. In this
chapter, an innovative ultra-wideband (UWB) bandpass filter with improved upper- stopband
performance is designed. The filter is very compact in size. The filter is executed using multiple
mode resonator (MMR). The three pairs of koch impedance-stepped stubs in shunt to a high
impedance microstrip line forms the MMR. Two interdigital coupled lines are used in the input
and output sides to improve the coupling degree. By altering the radius of the stars of the stubs,
the MMR resonant modes can be allocated within the UWB range (3.1 – 10.6 GHz) by
overpowering the counterfeit harmonics in the upper-stopband. The insertion loss is higher than
30.0 dB in the upper-stopband. The EM-simulated results are presented in this chapter.
46
5.2 Filter characterization
The proposed filter has a new topology of MMR which replaced the traditional MMR [13] [14].
The new topology of MMR is formed by attributing three pairs of star shaped impedance-stepped
stubs in shunt to a simple microstrip line which has high impedance, as shown in Figure 5. 1. And
the equivalent transmission line network is also shown in Figure 5. 2.
Figure 5. 1 Schematic of the UWB BPF
Figure 5. 2 Equivalent transmission line network for the proposed UWB BPF
47
Figure 5. 3 Simulated frequency responses of the proposed BPF
5.3 Dimensions of the filter
Parameters Value
R1 0.6 mm
R2 0.5 mm
Strip width 0.10 mm
Gap width 0.05 mm
Height of the PEC 0.05 mm
Length of the substrate 10 mm
Width of the substrate 14.8 mm
Height of the substrate 0.635 mm
Substrate permittivity εr = 10.8
Table 5. 1 Dimensions of the compact UWB filter
48
5.4 Simulated Results
The proposed filter configuration has typically contains three pairs of MMR which sits on a
substrate which is of thickness 0.635 mm and permittivity εr = 10.8. The structure of the filter is
shown in the following figures 5.1, and the s-parameter is shown in figure 5.3. The simulated
results shows that the filter has a passband at UWB frequency range and stopband over 12-30 GHz.
The predicted responses on insertion and return losses are shown in the figure 5.3.
5.5 Conclusion
In this chapter, a compact UWB filter is designed and simulated. This filter has enhanced stopband
performance. The filter is designed by using new multimode resonator method. The MMR is
formed by joining the three star shaped pairs to a high impedance microstrip line. The design
procedure is a bit complex when it is compared to rectangular MMRs [22] and circular MMRs
[21], but this star shaped design gives improved upper stopband performance when compared to
other MMRs.
It has a wide upper stopband with insertion loss more than 20 dB in the range of 14.5 to 30 GHz
is realized. This filter is very compact as its dimensions are 10 X 14.8 mm2.
49
CHAPTER SIX
Conclusion and Future work
5.1 Conclusion
The goal of this thesis is to investigate on some planar microwave bandpass filters. In this thesis
four novel compact bandpass filters has been designed and simulated, specifically five pole koch
resonators, two pole square loop resonator and compact UWB bandpass filter using MMR. The
design and simulation of each and every filter is given in detail with including all the required
specifications. From the previous research studies it is evident that, to design a good bandpass
filter there should be a smooth passband and good stopband with higher insertion loss in the
stopband. The four designs which are explained in this thesis has these important factors, which
makes these filters useful for the microwave applications. The conclusions of the designs are:
Koch fractal geometry is successfully applied in three designs, which gave the better results
compared with using other structures.
A new type of Open split koch loop resonator (OSKLR) has been developed and applied
to the different filter structures. This OSKLR structure is the backbone for the two designs
which are simulated successfully in this thesis.
Successfully transformed the conventional square loop resonator into Open split square
loop resonator. This open split square loop resonator successfully applied to the filter
structure.
50
Compact UWB bandpass filter has been designed effectively by using new type of MMRs.
This filter gave us the better upper stopband performance when compared to other
structures which containing different types of MMRs like circular MMR and square MMR.
6.2 Future Work
The prospects of the future work could be:
The four designs can be fabricated and their results should be compared with the simulated
results which are present in this thesis.
Computational electromagnetic modelling techniques like FDTD/FEM can be
implemented on the simulated designs.
After fabricating all the four filters, they should be applied in microwave applications to
check the performance of those filters in the real world.
This thesis is dedicated in designing particularly planar microwave bandpass filters with
the help of resonator circuits and MMRs. So, this work can be extended by designing other
type of planar microwave filters like advance RF/microwave filters, superconducting
filters, and tunable and reconfigurable filters.
51
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